# Brane-world Quantum Gravity

## TL;DR

This paper extends the canonical formulation of general relativity to brane-world scenarios, enabling a non-constrained quantum theory of brane geometries that could be tested experimentally and has implications for black holes and cosmology.

## Contribution

It develops a covariant canonical quantum gravity framework for brane-world models using Nash's embedding theorem, allowing for new insights into quantum geometry and potential experimental tests.

## Key findings

- Construction of a non-constrained canonical theory for brane-world quantum gravity
- Definition of quantum states via the Tomonaga-Schwinger equation in this context
- Potential experimental tests in astrophysics and laboratory settings

## Abstract

The Arnowitt-Deser-Misner canonical formulation of general relativity is extended to the covariant brane-world theory in arbitrary dimensions. The exclusive probing of the extra dimensions makes a substantial difference, allowing for the construction of a non-constrained canonical theory. The quantum states of the brane-world geometry are defined by the Tomonaga-Schwinger equation, whose integrability conditions are determined by the classical perturbations of submanifolds contained in the Nash's differentiable embedding theorem. In principle, quantum brane-world theory can be tested by current experiments in astrophysics and by near future laboratory experiments at Tev energy. The implications to the black-hole information loss problem, to the accelerating cosmology, and to a quantum mathematical theory of four-sub manifolds are briefly commented.